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Based on the observed high velocity of pulsars it is thought that neutronstars (NSs) receive a significant velocity kick at birth. Such natal kicks areconsidered to play an important role in the the evolution of binary-NS systems.The kick given to the NS (together with the effect of mass loss due to thesupernova explosion of the NS progenitor) may result in the binary disruptionor lead to a significant change of the binary orbital properties. Here weexplore in detail the dynamical aftermath of natal kicks in binary systems,determine their possible outcomes and characterize their relative frequency,making use of analytic arguments and detailed population synthesis models. In afraction of the cases the kick may cast the NS in such a trajectory as tocollide with the binary companion, or pass sufficiently close to it as todisrupt it (micro tidal disruption event; $\mu$TDE), or alternatively it couldbe tidally-captured into a close orbit, eventually forming an X-ray binary. Wecalculate the rates of direct post-kick physical collisions and the possiblepotential production of Thorne-Zytkow objects or long-GRBs through thisprocess, estimate the rates X-ray binaries formation and determine the rates of$\mu$TDEs and faint supernovae from white dwarf disruptions by NSs. Finally wesuggest that natal kicks can produce BH-NS binaries with very shortgravitational-wave merger time, possibly giving rise to a new type of promptlyappearing eLISA gravitational wave (GW) sources, as well as producing aLIGObinary-merger GW sources with a unique (likely type Ib/c) supernovaelectromagnetic counterpart which precedes the GW merger.

Neutron star natal kicks: Collisions, $\mu$TDEs, faint SNe, GRBs and GW sources with preceding electromagnetic counterparts